A mosquito is moving with a velocity  $\overrightarrow{v}$=0.5$t^2$ $\stackrel{\wedge }{i}$+3t $\stackrel{\wedge }{j}$+9 $\stackrel{\wedge }{k}$m/s and accelerating in uniform conditions. What will be the direction of mosquito after 2s?

$\begin{array}{l}\overrightarrow{v}=0.5t^2\widehat{i}+3t\widehat{j}+9\widehat{k}\\ At t = 2s,\\ \overrightarrow{v}=2\hat{i} + 6\hat{j} + 9\hat{k}\\ \left|\overrightarrow{v}\right|=\sqrt{2^2+6^2+9^2}=11\\ Hence, \hat{v}=\frac{\overrightarrow{v}}{\left|\overrightarrow{v}\right|}=\frac{2}{11}\hat{i} + \frac{6}{11}\hat{j} + \frac{9}{11}\hat{k}\\ With y axis, let say angle made is \beta ,\\ \cos \beta =\frac{6}{11}\\ \Rightarrow \beta ={\cos }^{-1}\left(\frac{6}{11}\right)\\ \end{array}$